So where can we see electrical energy traveling the other way, from matter into light? One example: a red hot electric burner shines light you can see. The light derives its energy from the vibrations or thermal energy of the matter. We normally don't think of it, but it turns out that your electric burner continues to shine even when the stove is at room temperature. The difference is that the room temperature stove emits light in colors that we can't see, down in the IR range.
If we imagine our conceptual chunk of matter as having oscillators that vibrate at all possible frequencies, it would be able to absorb or emit all the different frequencies of light. We have a word for that: we call that object a blackbody. The light that is emitted by a blackbody is called blackbody radiation. Objects at room temperature, like the turned-off burner, emit light in the IR spectrum. The Sun acts as a blackbody but because it is so warm it emits visible light. And of course, if an object radiates at some frequency, it must also absorb at that frequency, so a blackbody is a perfect IR absorber as well.
Blackbody radiation is made up of a characteristic distribution of frequencies (colors)of IR light. Figure 2.4 shows a plot with axes of the intensity of light in the y-direction and frequency in the x-direction. The units of intensity look a bit complicated; they are W/m2 wave number. The unit on the numerator is Watts (W), the same kind of Watts described by your hair dryers and audio amplifiers. A Watt is a rate of energy flow, defined as Joules per second, where energy is counted in Joules. The meters squared on the denominator is the surface area of the ground. The unit of wave numbers on the denominator allow us to divide the energy up according to the different wave number bands of light; for instance, all of the light between 100 and 101 cm-1 carry this many Watts per square meter of energy flux, between 101 and 102 cm-1 carry that
300 K
280 K
260 K
200 400 600 800 1000 1200 1400 1600 „2
Fig. 2.4 The intensity of light emitted from a blackbody as a function of light wave number, for different blackbody objects of different temperatures in Kelvins. A warmer object emits more radiation than a cooler one.
many, and so on. We can calculate the total flux of energy by adding up the bits from all the different slices of the light spectrum. The plot is set up so that we can add up the area under the curve to obtain the total energy intensity in Watts per square meter. You could cut the plot out with a pair of scissors and weigh the inside piece to determine its area, which would give you the total energy emitted over all the wave numbers of light.
The intensity of light at each frequency is called a spectrum. The IR light emission spectrum of a blackbody depends only upon the temperature of the blackbody. There are two things you should notice about the shapes of the curves in Fig. 2.4.
First, as the temperature goes up, the curves are getting higher, meaning that light at each frequency is getting more intense (brighter). When we start talking about planets we will need to know how much energy is being radiated from a blackbody in total, over all wavelengths. The units in Fig. 2.4 were chosen specifically so that the total energy being carried by all frequencies of light is equal to the area under the curve of the spectrum. As the temperature of the object goes up, the total energy emitted by the object goes up, which you can see from the fact that the curves in Fig. 2.4 get bigger. There is an equation which tells us how quickly energy is radiated from an object. It is called the Stefan-Boltzmann equation, and we are going to make extensive use of it. Get to know it now! The equation is
The intensity of light is denoted by I, and it represents the rate of energy emission from the object. The Greek letter epsilon (e) is the emissivity, a number between zero and one describing how good the blackbody is. For a perfect blackbody, e = 1. Sigma (a) is a fundamental constant of physics which never changes, a number you can look up in reference books, called the Stefan-Boltzmann constant. T is the temperature in Kelvins, and the superscript 4 is an exponent indicating that we have to raise the temperature to
the fourth power. The Kelvin temperature scale begins with 0 K when the atoms are vibrating as little as possible, a temperature called absolute zero. There are no negative temperatures on the Kelvin scale.
One of the many tricks of thinking scientifically is to pay attention to units. Let us examine Eqn. (2.1) again, with units of the various terms specified in the brackets.
W m2
2 K4
The unit of energy flux is Watts (W), equal to Joules of energy per second. The meters squared on the bottom of that fraction is the surface area of the object that is radiating. The area of the earth, for example, is 5.14 ■ 1014 m2. Here's what I wanted to point out: the units on either side of this equation must be the same. On the right-hand side, K4 cancels leaving only W/m2 to balance the left-hand side. In general, if are unsure about relating one number to another, the first thing to do is to listen to the units. We will see many more examples of units in our discussion, and you may rest assured I will not miss an opportunity to point them out.
IR-sensitive cameras allow us to see what the world looks like in IR light. The cheeks of the guy in Fig. 2.5 are warmer than the surface of his glasses, which are presumably at room temperature. We can estimate how much more light is shining from the cheeks than from the glass surface using Eqn. (2.1), to be icheek _ echeeka ^^leek
passes eglassesa ^glasses
The Stefan-Boltzmann constant a is the same on both top and bottom; a never changes. The emissivity e might be different between the cheek and the glasses, but let's assume
that they are the same. This leaves us with the ratio of the brightnesses of the skin and glasses equal to the ratio of temperatures to the fourth power, maybe (285 K/278 K)4, which is about 1.1. The cheeks shine 10% more brightly than the surface of the coat, and that is what the IR camera shows us.
The second thing to notice about the effect of temperature on blackbody spectra in Fig. 2.4 is that the peaks shift to the right as temperature increases. This is the direction of higher frequency light. You already knew that a hotter object generates shorter wavelength light because you know about red hot and white hot. Which is hotter? White hot, of course; any kid on the playground knows that. An object at room temperature (say 273 K) glows in the IR range, which we can't see. A stove at stovetop temperatures (400-500 K) glows in shorter wavelength light, which begins to creep up into the visible part of the spectrum. The lowest energy part of the visible spectrum is red light. Get the object hotter, say the temperature of the surface of the Sun (5000 K), and it will fill all wavelengths of the visible part of the spectrum with light. Figure 2.6 compares the spectra of the Earth and the Sun. You can see that sunlight is visible whereas "earth light" (also referred to as terrestrial radiation) is in the IR spectrum. Of course, the total energy flux from the Sun is much higher than it is from Earth. Repeating the calculation we used for the IR photo, we can calculate the ratio of the fluxes as (5000 K/273 K)4, or about 105. The two spectra in Fig. 2.6 have been scaled by dividing each curve by the maximum value that the curve reaches, so that the top of each peak is at a value of one. If we hadn't done that, the area under the Earth spectrum would be 100,000 times smaller than the area under the Sun spectrum, and you would need a microscope to see the Earth spectrum on Fig. 2.6.
It is not a coincidence that the Sun shines in what we refer to as visible light. Our eyes have evolved to be sensitive to visible light. The IR light field is a much more complicated thing for an organism to measure and understand. For one thing, the eyeball, or whatever light sensor the organism has, will be shining IR light of its own. The organism measures light intensity by measuring how intensely the incoming light deposits energy into oscillators coupled to its nervous system. It must complicate matters if the oscillators lose energy by radiating light of their own. IR telescopes must be cooled in order to make accurate IR intensity measurements. Snakes are capable of sensing IR light. Perhaps this is useful because their body temperatures are colder than those of their intended prey.
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Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.